The invention relates to a method for the production of Gaussian intensity distributions in the beam profile of radiation generated by nonlinear optical processes in terms of the classifying clause of claim 1.
A fundamental requirement of laser applications consists of beam profiles exhibiting a defined radial intensity distribution. The intensity distribution of the radiation in a transverse section is designated as the beam profile thereof. The commonest form of the required radial distribution is that of a rotationally symmetrical Gaussian function according to the formula
E(r)=E0e(xe2x88x92r2/w2)
It is of significance that Gaussian intensity distribution reoccurs in the laser beam generated in the course of frequency conversion by non-linear optical processes.
The most important non-linear optical materials for non-linear optical processes are crystals, with the result that outstanding significance is attributed to these materials.
The intensity distribution or the beam profile of a laser beam generated in a non-linear optical process is dependent on the beam profile of the impinging radiation, the wavelengths of the light participating as well as the crystal properties, such as refractive index, birefringence angle and interaction length. Since the impinging and generated laser beams do not usually have the same wavelength, the dispersive properties of the crystal have an effect. This generally induces spatial separation of the generated and impinging waves in the direction of the optical axis of the crystal. This effect, commonly designated as the walk-off effect, is generally known as an effect limiting the efficiency of non-linear optical processes (A. Ashkin, G. D. Boyd, J. M. Dzieduc in: IEEE Journ. Quantum Electronics, QE-2, No. 6 (1966); S. Bouroix, M. D. Plimmer, F. Nez, L. Julien, F. Biraben in: Opt. Comm., Vol. 99 (1993)).
In addition to the above, the walk-off effect has influence on the beam profile of the wave generated. As shown in FIG. 1, the progressive divergence of the beam generated from the impinging beam along the path of the beams within the crystal leads to a divergence of the beam profile of the wave generated in the direction of the optical axis 8 of the crystal 1. As an example thereof, a long stretched-out and more rectangularly distorted beam profile than that of the Gaussian beam profiles of the impinging waves emerges at the exit from crystal 1 (FIG. 2). A fundamental difference has to be made, here, between the beam profile in the so-called near field 13 and the remote field 12 (FIG. 2). This terminology arises from the propagation theory of monochromatic, coherent electromagnetic radiation and demarcates the region in which the circumstances of the light generation play a part, the near field from the adjoining region, the remote field. In typical laser applications, the near field involves an optical path length of between a few mm and 1 m behind the source of radiation. Along this path, the beam profile changes from that shown in FIGS. 1 and 2 to an astigmatic profile with Gaussian intensity distribution. Astigmatic signifies that the beam profile has different beam parameters such as beam diameter and divergence in the horizontal and vertical directions.
It becomes particularly clear that the said transition process from near to remote field does not proceed without further disturbance if an optically refractive surface with an imaging effect is introduced a short distance behind the crystal. In the application of resonators for instance, the positioning of a generally plano-concave mirror at a short distance behind the crystal is absolutely necessary for the correct functioning of the resonator. Although the reflective coating of the said mirror is transparent for the frequency converted radiation, the imaging effect of the curved surface also remains in place for the converted radiation. The mirror thus has the effect of a divergent lens and shifts the transition of the beam profile to the remote field up to infinity under certain circumstances, depending on the curvature of the lens. This implies that where frequency conversion in crystals, particularly in the application of resonators, is involved, beam profiles exhibiting several intensity peaks with intermediate sections (FIG. 2) are to be found within the distance range of up to several meters important for application of the converted radiation. The aforementioned are not Gaussian intensity distributions at all and are thus entirely unsuitable for many applications. The use of frequency converted radiation, particularly in resonators, has thus been severely restricted up till now for this reason
The objective of the invention is thus the development of a method generic with the independent claim by means of which it can be warranted that the beam profile of the radiation generated and transformed by the walk-off effect and subsequent transition from near to remote field be converted into a rotationally symmetrical, particularly a circular beam profile with Gaussian intensity distribution. Achievement of the objective is indicated in the features of claim 1. According to the above, a decoupled radiation beam from the non-linear optical material within a light path of length defined by the near to remote field transition of the decoupled radiation is only influenced by a system comprised of at least one optically refractive surface, which has no overall imaging effect. The beam parameters of the decoupled harmonic wave, such as beam diameter and divergence, is changed by the optically refractive surfaces, for example several cylindrical or spherical lenses, in such a way that the desired, particularly circular, Gaussian intensity distribution of the beam profile results. By way of example, only the beam parameters of the horizontal planes can be adjusted to those of the vertical planes by means of cylindrical lenses. The use of optical resonators for frequency conversion, particularly for frequency doubling, prevents any change in the near to remote field transition effected by the type of beam decoupling applied. Any influences involved in the decoupling process are compensated by the effect of optically refractive surfaces with opposed curvature such as that of the decoupling mirror.